{"id":256219,"date":"2025-07-16T07:40:59","date_gmt":"2025-07-16T07:40:59","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=256219"},"modified":"2025-07-16T07:41:02","modified_gmt":"2025-07-16T07:41:02","slug":"you-are-given-the-following-information-about-y-and-dependent-variable-independent-variable-in-addition-the-least-squares-method-yielded-the-following-equation-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/16\/you-are-given-the-following-information-about-y-and-dependent-variable-independent-variable-in-addition-the-least-squares-method-yielded-the-following-equation-2\/","title":{"rendered":"You are given the following information about y and Dependent Variable Independent Variable In addition, the least squares method yielded the following equation"},"content":{"rendered":"\n<p>You are given the following information about y and Dependent Variable Independent Variable In addition, the least squares method yielded the following equation: y = 12.06 + 0.12x Calculate the value of SSE; round your answer to three decimal places.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To calculate the <strong>Sum of Squared Errors (SSE)<\/strong>, we need a set of actual values of the dependent variable (<strong>y<\/strong>) and corresponding independent variable values (<strong>x<\/strong>). The regression equation provided is:<\/p>\n\n\n\n<p><strong>y = 12.06 + 0.12x<\/strong><\/p>\n\n\n\n<p>This equation is used to compute the predicted y-values (<strong>\u0177<\/strong>) for each observed x-value. The formula for SSE is:<\/p>\n\n\n\n<p><strong>SSE = \u03a3(y &#8211; \u0177)\u00b2<\/strong><\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>y<\/strong> is the actual value,<\/li>\n\n\n\n<li><strong>\u0177<\/strong> is the predicted value,<\/li>\n\n\n\n<li>The difference (y &#8211; \u0177) is the error,<\/li>\n\n\n\n<li>Each error is squared,<\/li>\n\n\n\n<li>The sum of these squared differences gives the SSE.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Without actual data:<\/h3>\n\n\n\n<p>If only the regression equation is given and no values of <strong>x<\/strong> and <strong>y<\/strong>, it is <strong>not possible<\/strong> to calculate the SSE directly. SSE depends on the individual deviations between observed values and the values predicted by the regression model.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Example with data:<\/h3>\n\n\n\n<p>Suppose we are given this data set:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>x<\/th><th>y<\/th><\/tr><\/thead><tbody><tr><td>10<\/td><td>13.5<\/td><\/tr><tr><td>20<\/td><td>14.2<\/td><\/tr><tr><td>30<\/td><td>15.1<\/td><\/tr><tr><td>40<\/td><td>15.8<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Using the regression equation y = 12.06 + 0.12x, we calculate predicted values:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For x = 10: \u0177 = 12.06 + 0.12(10) = 13.26<\/li>\n\n\n\n<li>For x = 20: \u0177 = 12.06 + 0.12(20) = 14.46<\/li>\n\n\n\n<li>For x = 30: \u0177 = 12.06 + 0.12(30) = 15.66<\/li>\n\n\n\n<li>For x = 40: \u0177 = 12.06 + 0.12(40) = 16.86<\/li>\n<\/ul>\n\n\n\n<p>Now calculate SSE:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(13.5 &#8211; 13.26)\u00b2 = 0.0576<\/li>\n\n\n\n<li>(14.2 &#8211; 14.46)\u00b2 = 0.0676<\/li>\n\n\n\n<li>(15.1 &#8211; 15.66)\u00b2 = 0.3136<\/li>\n\n\n\n<li>(15.8 &#8211; 16.86)\u00b2 = 1.1236<\/li>\n<\/ul>\n\n\n\n<p>SSE = 0.0576 + 0.0676 + 0.3136 + 1.1236 = <strong>1.562<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p><strong>SSE = 1.562<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-598.jpeg\" alt=\"\" class=\"wp-image-256221\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>You are given the following information about y and Dependent Variable Independent Variable In addition, the least squares method yielded the following equation: y = 12.06 + 0.12x Calculate the value of SSE; round your answer to three decimal places. The Correct Answer and Explanation is: To calculate the Sum of Squared Errors (SSE), we [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-256219","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/256219","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=256219"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/256219\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=256219"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=256219"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=256219"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}